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# A gumball machine contains between 90 and 100 gumballs. If

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Senior Manager
Joined: 02 Oct 2005
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A gumball machine contains between 90 and 100 gumballs. If  [#permalink]

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24 Oct 2005, 10:03
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A gumball machine contains between 90 and 100 gumballs. If
the machine is set to dispense 4 gumballs at a time, 2
gumballs will be left in the machine. If the machine is set
to dispense 5 gumballs at a time, 3 gumballs will be left in
the machine. How many gumballs are in the machine?

A. 90
B. 92
C. 94
D. 96
E. 98

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VP
Joined: 30 Sep 2004
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24 Oct 2005, 10:09
98...

4 balls at a time leaves a remainder of 2 and 5 balls at a time leaves a remainder of 3. only 98 fits...
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

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Manager
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24 Oct 2005, 10:12

If:
g = # of gumballs
90 <= g <= 100
g/4 has a remainder of 2
9/5 has a remainder of 3

For g/4 to have a remainder of 2, g must equal 90, 94, or 98
(88, 92, and 96 are multiples of 4, so g must be 2 greater than one of those numbers)

For g/4 to have a remainder of 3, g must equal 93 or 98 (3 greater than 90 or 95, which are multiples of 5)

The common number here is 98, so g=98.

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Senior Manager
Joined: 02 Oct 2005
Posts: 297

Kudos [?]: 24 [0], given: 0

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24 Oct 2005, 14:27
OA is E and here is the explanation:

The multiples of 4 that could produce a result between 90 and 100 are
88 (88 + 2 = 90)
92 (92 + 2 = 94)
96 (96 + 2 = 98)

The multiples of 5 that could produce a result between 90 and 100 are
90 (90 + 3 = 93)
95 (95 + 3 = 98)

The only result the two sets have in common is 98.

Kudos [?]: 24 [0], given: 0

24 Oct 2005, 14:27
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